{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NFXOEULCXWN7FY7YXGW3HAOGM3","short_pith_number":"pith:NFXOEULC","schema_version":"1.0","canonical_sha256":"696ee25162bd9bf2e3f8b9adb381c666c462216a9e734c4494bcbd0ed4ac0204","source":{"kind":"arxiv","id":"1412.0736","version":1},"attestation_state":"computed","paper":{"title":"Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kohei Suzuki","submitted_at":"2014-12-01T23:39:05Z","abstract_excerpt":"We introduce a new distance, a Lipschitz-Prokhorov distance $d_{LP}$, on the set $\\mathcal {PM}$ of isomorphism classes of pairs $(X, P)$ where $X$ is a compact metric space and $P$ is the law of a continuous stochastic process on $X$. We show that $(\\mathcal {PM}, d_{LP})$ is a complete metric space. For Markov processes on Riemannian manifolds, we study relative compactness and convergence."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.0736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-01T23:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"8e2601e590aa0b44ad0d5c567a0bd68a9ce25e540ff2d5c893d7b2635582ebf0","abstract_canon_sha256":"393d547cb6dd828c38df7117d51c54051099c56781cf1c3b93ef928ec9e80b04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:21.295557Z","signature_b64":"XHtokj1UlahgTCWTE5wRpdWgGmKsS9xqudcMkL8kS2+KykXlcf6GZnFqu5xQOhyFQXDSWVperIJ5rn+4sMClAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"696ee25162bd9bf2e3f8b9adb381c666c462216a9e734c4494bcbd0ed4ac0204","last_reissued_at":"2026-05-18T02:32:21.295172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:21.295172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kohei Suzuki","submitted_at":"2014-12-01T23:39:05Z","abstract_excerpt":"We introduce a new distance, a Lipschitz-Prokhorov distance $d_{LP}$, on the set $\\mathcal {PM}$ of isomorphism classes of pairs $(X, P)$ where $X$ is a compact metric space and $P$ is the law of a continuous stochastic process on $X$. We show that $(\\mathcal {PM}, d_{LP})$ is a complete metric space. For Markov processes on Riemannian manifolds, we study relative compactness and convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0736","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.0736","created_at":"2026-05-18T02:32:21.295229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0736v1","created_at":"2026-05-18T02:32:21.295229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0736","created_at":"2026-05-18T02:32:21.295229+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFXOEULCXWN7","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFXOEULCXWN7FY7Y","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFXOEULC","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3","json":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3.json","graph_json":"https://pith.science/api/pith-number/NFXOEULCXWN7FY7YXGW3HAOGM3/graph.json","events_json":"https://pith.science/api/pith-number/NFXOEULCXWN7FY7YXGW3HAOGM3/events.json","paper":"https://pith.science/paper/NFXOEULC"},"agent_actions":{"view_html":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3","download_json":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3.json","view_paper":"https://pith.science/paper/NFXOEULC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0736&json=true","fetch_graph":"https://pith.science/api/pith-number/NFXOEULCXWN7FY7YXGW3HAOGM3/graph.json","fetch_events":"https://pith.science/api/pith-number/NFXOEULCXWN7FY7YXGW3HAOGM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3/action/storage_attestation","attest_author":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3/action/author_attestation","sign_citation":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3/action/citation_signature","submit_replication":"https://pith.science/pith/NFXOEULCXWN7FY7YXGW3HAOGM3/action/replication_record"}},"created_at":"2026-05-18T02:32:21.295229+00:00","updated_at":"2026-05-18T02:32:21.295229+00:00"}